An asymptotic matching approach to shallow-notched structural elements

作者：Cornetti Pietro^*; Taylor David; Carpinteri Alberto

来源：Engineering Fracture Mechanics, 2010, 77(2): 348-358.

DOI：10.1016/j.engfracmech.2009.04.013

• Shallow notches
• V-notches
• Multiscale analysis
• Asymptotic matching
• Brittleness number
• Finite fracture mechanics

Fracture in brittle material specimens with V-notches is satisfactorily described assuming as governing parameter the generalized (or notch) stress intensity factor, whose anomalous physical dimensions depend on the notch opening angle. Its critical value, i.e. the generalized toughness, can then be linked to the material strength and toughness according to a number of fracture criteria available in the literature. However. all these criteria provide an infinite failure load as the notch depth tends to zero, this undesirable property being shared with Linear Elastic Fracture Mechanics when applied to vanishing cracks. Aim of the present paper is to overcome this shortcoming. The analysis of the notched specimens is carried out by means of a multiscale approach according to which the problem is solved separately in the region far away from the notch (the outer field) and in the region close to the notch (the inner field). Hence, the asymptotic matching technique can be exploited to achieve the overall solution Although the procedure is general. i.e. it may be applied to any notch shape, numerical computations refer to sharp V-notches with a re-entrant corner equal to 120 degrees. Comparison with experimental data obtained by testing polystyrene specimens turns out to be more than satisfactory.

• 出版日期2010-1